# What is Archimedes: Definition and 211 Discussions

Archimedes of Syracuse (; Ancient Greek: Ἀρχιμήδης; Doric Greek: [ar.kʰi.mɛː.dɛ̂ːs]; c. 287 – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral.His other mathematical achievements include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the siege of Syracuse, where he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested be placed on his tomb to represent his mathematical discoveries.
Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes written by Eutocius in the 6th century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance and again in the 17th century, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

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1. ### Student Recreates the Archimedes Death Ray

Student Recreates the Archimedes Death Ray https://www.giantfreakinrobot.com/sci/ancient-death-ray-recreated.html
2. ### I A specific case of an exception to Archimedes' Principle?

First post on this forum, hopefully in the correct category and conforming to forum rules. Will the object in below scenario move upwards, downwards or will it remain stationary? An object is submersed in a container 'A' which contains a fluid 'B' (e.g. water) The trapezium shaped object...
3. ### I Exploring the Casimir Effect: The Archimedes Experiment

Vacuum energy is predicted by Quantum Field Theory, and also independently corroborated by recent observations in cosmology involving accelerated expansion. More corroboration occurs in superconducting cuprates exhibiting quantum criticality, and in the Casimir effect The island of Sardinia...
4. ### B Archimedes Principle - A Rock and Water Magic Trick

I understand how to measure specific gravity of a rock. One weighs the rock then tares a beaker of water and then suspends the rock on a string to observe the “weight” gain of displaced water. My brain however could never get how, without adding a drop more water or adding the mass of the rock...
5. ### Doing experiment to find the authenticity of Archimedes' law

I have solved the question like this: Since Volume=Upthrust We need to find the upthrust and the volume V. To find the volume, we will submerge the block in the water and find the difference. To find the upthrust F, we will subtract the weight (finding the weight usinf newton-meter) from the...

7. ### Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg

The result is supposed to be 12,2 m but every time I get 8,016 m... I used for example this formula >r=m/[(density of air-density of hot air)*(4/3)*pi] For density I used > rho=(p*M)/(R*T) Am I forgetting something? Thanks in advance.
8. ### I A proof of Archimedes' Principle

Hi All, is there a proof to Arquimedes Principle and the expression for the buoyancy force? In case there is a proof, may we refer to this as Arquimedes theorem? (Buoyancy force = density of the fluid x acceleration of gravity x submerged volume) Best Regards, DaTario
9. ### MHB Physics - Archimedes principle

Im having trouble with the following question regarding Archimedes principle. A wooden board with an area of 4.55m^2 is dropped into the dead sea (P sea- 1240 kg/m^-3). Calculate the proportion that would float above the surface. (P wood - 812 kg/m^-3). My understanding is that the volume (V...
10. ### Buoyant Force and Archimedes' Principle

Hello there, I have a quite different approach on answering the part c and d of this problem. Can you guys help me to see if my method is acceptable or logical? (I got the same answers as the back of the textbook, however my methods differ from the solutions manual). Here is my answer/attempt at...
11. ### Archimedes Strength: What Determines Strength?

What determines the strength of Archimedes ?
12. ### B Could Archimedes' problem have been solved a little differently?

When I was reading this page to understand Archimedes' 'story' I got a question: http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html#buoy According to the example shown, Archimedes found the density of crown by finding the apparent weight. What if he had just measured the volume of water...
13. ### General Query on Archimedes' Principle

I had some questions about Archimedes' Principle. This image shows an object being gradually submerged into fluid: As far as I'm aware, when the object is floating, weight of fluid displaced by object = upthrust acting upwards on the object. When the object is fully submerged, volume of the...
14. ### Drag force on a descending sphere

i tried a force balance around the sphere but the weight of the displaced fluid is greater than the weight of the sphere which gives a net acceleration upwards and no terminal velocity but the book says that the terminal velocity has a certain value from there the exercise is meaningless to me...
15. ### B How does the weight on a scale change when an object is submerged in water?

Dear, I am a medical doctor and my physics background is limited to that of secondary school many years ago, but should want to ask for your help. In attachment, you can find a picture of my question. On a scale, we place a jar filled with water. We place in the water a platform which is...
16. ### B A question about one of Archimedes' works

I was reading "Significant Figures: The Lives and Work of Great Mathematicians" by Ian Stewart. The following is an excerpt from its chapter on Archimedes: So, the first one was that he proved the surface area of a sphere ##= 4\pi r^2##. The second one is the result that the volume of a sphere...
17. ### MHB Exploring How Archimedes Discovered Quadrature of the Parabola w/o Calculus

How did Archimedes discover the Quadrature of the parabola without the use of calculus? If someone could please explain, I would be eternally grateful.
18. ### Engineering Using the Archimedes Principle to do calculations for this floating buoy

A Spherical buoy has a diameter of 2m and weighs 3kN. It is designed to be used in a variety or circumstances by it being floated in water and anchored to the floor with a chain. Draw the free body diagram and determine the following given that the volume of a sphere is, Volume = πD3/6 The...
19. ### B Is this method of estimating Pi too similar to Archimedes' method?

The recurrence relation was given as: ##p_k=2^{k+1}\cdot h_k## where ##h_0^2=2## ##h_{k+1}^2=(\frac{1}{2}h_k)^2+(1-\frac{1}{2}h_k \cdot \cot(2^{-k}\cdot \alpha))^2## and ##\alpha=\arctan(1)##. This is not exactly an original or noteworthy derivation, is it? I feel that it's been done...
20. ### Buoyancy and the Archimedes Principle

Hello all I was hoping someone could help me with some intuition regarding Buoyancy and Archimedes Principle. I thought i understood Buoyancy in terms of pressure but when i came across Archimedes Principle I realized I did not fully understand what Buoyancy is. I have an object that is a...
21. ### Olds Elevator vs Traditional Archimedes Screw

This device... ... is purportedly superior to the more traditional Archimedes lift where the screw is rotated and the tube is stationary. The video itself does not explain the comparative physics very thoroughly. From the video itself and from the comments section, three broad types of...
22. ### B Melting Ice Caps and Sea Level Rise: Separating Fact from Fiction

I'm pretty sure that everyone knows that if you put an ice cube in a cup of water, and leave it for some time for the ice to melt, the level of water in the glass will not rise. (you could use that principle where that guy was in the tub and said "Eureka!" and then ran around naked). Now, my...
23. ### Buouyancy force and Archimedes' principle

How much more will the volume of a fishingboat go under water, if I load the boat with 3.0m^3 fish with the density 0.90kg/dm^3? Fish : 3.0m^3 Density of fish: 0.90kg/dm^3? Homework Equations Archimedes principle: density * volume * g[/B]The Attempt at a Solution Tried setting upward force...
24. ### Archimedes' principle -- Which box will sink first as we add coins....

There are five empty box contains with the same weight. The upper side of each boxes are removed. These boxes are floating in a pool of water. Then to each box we put coins slowly one by one. Assuming the box does not tilt. Determine which of the following size of the box (p x l x t) can be...
25. ### Solve Archimedes Problem: Find Crown's Density

I have got a question in my physics book.The question goes like that: (Let's suppose the weight of the gold crown of Archimedes is 10 kg in air and 9.4 kg when immersed in water.What is the density of the crown? ) The solution says: If the volume of the crown is V and density is p then, Vp=10 kg...
26. ### Submarine Buoyancy Differential Equation

Homework Statement A submarine of mass 80 000 kg is floating at rest (neutrally buoyant) at a depth of 200 m in sea water. It starts pumping out sea water from its ballast tanks at a rate of 600 litres per minute, thus affecting both its mass and the buoyancy force. Determine the vertical...
27. ### B Archimedes principle and the density of a rock

Hi, so I have a problem that I am working on and I think that I understand Archimedes principle but the density that I am calculating is just absurd. The problem is as follows: "A geologist finds that a moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water...
28. ### Volume using Archimedes Method

Homework Statement Homework Equations Volume of Sphere = 4/3 pi r^3 d = m/v The Attempt at a Solution my attempt is: r = 2 Vsphere = 32/3 pi cm^3 density of mercury = 13.53 g/ml d*v of sphere = 259.7grams 259.7 grams of sphere * (1/density of mercury) = 259.7g *( 1 ml / 13.53 g) = 19.2 ml...
29. ### B Archimedes' Principle for gases - derivation?

Hi all, I understand where Archimedes' Principle comes from in liquids: If we imagine a cylinder immersed in a liquid of density ρ whose cross-sectional area is A and whose top is at depth h1 and whose bottom is at depth h2: Force(top of cylinder) FT = ρgh1A Force(bottom of cylinder) FB =...
30. ### Archimedes Principle and steel bar question

Homework Statement Can someone tell me if i have done this correct please? A steel bar of length 0.6m and diameter 70mm is suspended from a chain and lowered into a tank of liquid whose relative density is 0.9. Determine the tension in the chain when the bar is fully immersed. The density of...
31. ### Using Archimedes' principle in engineering applications

Homework Statement A cylindrical buoy floats in sea water with its axis vertical so that it's three-fourths submerged. The buoy is 0.8m in diameter and 2m in height. Its fabricated from iron plate 10mm thick. Calculate the mass of iron chain securing the buoy. The relative density of iron is...
32. A

### Archimedes' Principle and a weather balloon

Homework Statement 2. Homework Equations Buoyant force= mg(mass of fluid displaced = Vpg (volume of fluid displaced) Buoyant force=weight of object (if floating) The Attempt at a Solution If the total mass is 99kg, then the total force acting downwards is 990N. It also said that the balloon...
33. ### I Theorem behind Archimedes principle of buoyancy?

I was thinking about why the buoyant force on an object should depend solely on it's volume and not shape. It seems loosely like the divergence theorem in that an integral over the surface is determined by the volume. There is a big difference though; in the divergence theorem we integrate...
34. ### Exploring Archimedes Principle: A Step-by-Step Demonstration

Homework Statement Hi, in my high school physics class we have to teach (part of) a lesson, mine being archimedes principle, and we have to make a demonstration of our topic. My idea was to show how you can calculate the buoyant force on a immersed object with the weight of the water it...
35. ### Weight and the Archimedes Principle

I was wondering - if you had a container of water and you push a hollow object that is buoyant to the bottom so that it is completely immersed - the whole container will be heavier because of water being displaced up in the container. Now if you release your hand or whatever you use to hold the...
36. ### Archimedes Principle: Pure gold or not?

Homework Statement Archimedes, prove your stuff. A royal crown (cola?) of pure gold is suspended in air by a thread and the tension in the thread is of magnitude T. When the crown is totally immersed in water, the magnitude of the tension in the thread is 0.872T. A) sketch a second law force...
37. ### Fluid Mechanics and Archimedes Principle

Homework Statement [/B] A rectangular object has a width of 40 meters, height of 15 meters, and length of 2 meters. It floats consistently when 3 meters of its height is below the surface of the water. 1. Find the volume of the displaced water. 2. How much is the buoyant force on the object...
38. ### Archimedes and Maritime Engineering

I'm wondering if its demonstrable that Archimedes Principle led to growth in Maritime engineering. Does anyone have any advice on where one could look to find information on ship building 2200 years ago?
39. ### I Something about Archimedes' Principle

Hello, I was reading about Archimedes' Principle on the wiki ( https://en.wikipedia.org/wiki/Archimedes%27_principle ) and a question popped up regarding the upthrusting force (also called buoyant force) that the liquid exerts on an object that is in the liquid. I understand that the...
40. ### B Generalization of Archimedes' Trammel?

The Trammel of Archimedes has been around for a long time, but it is usually with two "lanes", or shuttles. Some variations on the classical one are covered nicely in "A New Look at the So-Called. Trammel of Archimedes" byTom M. Apostol and Mamikon A. Mnatsakanian...
41. ### Physics Archimedes Principle Distance an object sinks

Homework Statement A block of wood measures 2.2m by 2.5m with depth 3.6m with weight 102KN. When placed in water, how far will it sink? g = 9.81 ms-2 density of water = 1000kg m-3 Homework EquationsThe Attempt at a Solution Volume = 2.2(2.5)(3.6) = 19.8m3 Mass = 102000 / 9.81 = 10398 kg...
42. ### Archimedes Principle: Calculating Relative Density for a Block of Oak and Lead

. Homework Statement A block oak weighs 90 N in air. A piece of lead weighs 130 N in water. The two weigh together 100N in water. Calculate the relative density of the wood.Homework Equations F=mxg F(archimedes)= density x Volume x g The Attempt at a Solution F (g)oak = 90 N F= mxg m= 90N/9.81...
43. ### Archimedes principle and passing gas

I used a tub for my hemorrhoid. I learned the archimedes principle which the buoyant force is equal to the mass of water displaced. The tub was filled with water 4/5. I accidently farted in a tub and suddenly the water flew into the hole which is located on the top of tub.does the fart gas...
44. ### Archimedes' Buoyancy: Which Ball Will Experience a Greater Buoyant Force?

Question: Balls A and B of equal mass are floating in a swimming pool, as shown below. Which will produce a greater buoyant force? (Image shows two circles with circle A larger than circle B) A. Ball A B. Ball B C. The forces will be equal D It is impossible to know without knowing the volume...
45. ### Archimedes principle boat displacement

Homework Statement 35m^3 of a boat's volume is submerged under water. What does the boat weigh? The boat is 14 metres long. Homework Equations pVg=mg The Attempt at a Solution pVg=mg pV=m m=pV=1000*35 This is what my teacher said, but I don't understand it. The submerged volume of the boat...
46. ### Archimedes' area of a sphere proof; proposition 2

Hi, I wanted to see if I could understand Archimedes' proof for the area of a sphere directly from one of his texts. Almost right away I was confused by the language. Archimedes lists a bunch of propositions that eventually lead up to the 25th proposition where the area of the sphere is finally...
47. ### Understanding Buoyancy: The Limits of Archimedes

jfizzix submitted a new PF Insights post Understanding Buoyancy: The Limits of Archimedes Continue reading the Original PF Insights Post.
48. ### Solving Force Exerted by Liquid Using Archimedes Principle

Homework Statement Homework EquationsThe Attempt at a Solution Applying Archimedes priniciple the force exerted by liquid on the upper hemisphere would be ## F = \frac{2}{3}\pi R^3 \rho g## . Now I am not sure , what does it mean by force due to gauge pressure ? Any help is appreciated ...
49. ### Experimental Error in Archimedes Principle Lab

Homework Statement I need to find three potential reasons for my .5% error in a lab where I used the Archimedes Principle to measure the density of Iron. We only used a graduated cylinder full of water and an iron mass. I measured the water level from the meniscus. We used two different...
50. ### What is Archimedes' Principle?

Homework Statement Can somebody please tell me exactly what archimedes prnciple is? Homework Equations The Attempt at a Solution [/B] So, I watched this video: . Apparently if we have a cube in a bucket of water then the mass of the whole cube is equal to the mass of the displaced water...